Question: Simplify the following expression: $t = \dfrac{n^2 + 8n + 15}{n + 3} $
Solution: First factor the polynomial in the numerator. $ n^2 + 8n + 15 = (n + 3)(n + 5) $ So we can rewrite the expression as: $t = \dfrac{(n + 3)(n + 5)}{n + 3} $ We can divide the numerator and denominator by $(n + 3)$ on condition that $n \neq -3$ Therefore $t = n + 5; n \neq -3$